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Simplifying x2 + -6.5x + -12 = 0 Reorder the terms: -12 + -6.5x + x2 = 0 Solving -12 + -6.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -6.5x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -6.5x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -6.5x + x2 = 0 + 12 -6.5x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -6.5x + x2 = 12 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = 12 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 12 + 10.5625 Combine like terms: 12 + 10.5625 = 22.5625 10.5625 + -6.5x + x2 = 22.5625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 22.5625 Calculate the square root of the right side: 4.75 Break this problem into two subproblems by setting (x + -3.25) equal to 4.75 and -4.75.Subproblem 1
x + -3.25 = 4.75 Simplifying x + -3.25 = 4.75 Reorder the terms: -3.25 + x = 4.75 Solving -3.25 + x = 4.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 4.75 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 4.75 + 3.25 x = 4.75 + 3.25 Combine like terms: 4.75 + 3.25 = 8 x = 8 Simplifying x = 8Subproblem 2
x + -3.25 = -4.75 Simplifying x + -3.25 = -4.75 Reorder the terms: -3.25 + x = -4.75 Solving -3.25 + x = -4.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -4.75 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -4.75 + 3.25 x = -4.75 + 3.25 Combine like terms: -4.75 + 3.25 = -1.5 x = -1.5 Simplifying x = -1.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {8, -1.5}
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